How do I have an exception to a material override?
You can use the Pass Index to indicate to the material how to treat specific objects in your scene.
For those objects you want highlighting, set the Pass Index to a specific value (in this case, '1') :

In your material, use the Object Info node to get the Object Index and compare it to determine how to shade your object (in this case I've used the result of the compare to choose between colours in a MixRGB node) :

This produces the following result (with the cube set to index '1' and everything else left at index '0') :

To change the highlighted object, simply update the Pass Index to disable the previously highlighted one and enable the new one.